Development of New Dimension-Reduction Methods for Reliability, Simulation, and Design of Complex Engineering Systems

本研究项目的目标是开发新的计算方法，用于复杂工程系统的不确定性传播、可靠性分析和设计优化。提出的工作将基于：(1)计算随机响应的二阶矩特征的新降维方法；(2)基于降维和矩的可靠性随机分析新方法；(3)基于可靠性/鲁棒性的结构和机械系统优化设计新算法。所提出的方法是新颖的，将能够解决高度非线性的输入-输出变换；无限数量的随机变量或过程；和任意大的不确定性输入，但可以准确地预测响应矩和可靠性。潜在的工程应用包括地面车辆耐久性设计；航空航天结构疲劳与断裂设计；并设计微电子封装系统。从基本的观点来看，降维方法将为任意区域上的一般多维积分提供准确而有效的解。因此，基础科学和应用科学中涉及不确定性和/或需要对这些积分进行评估的许多问题将通过本项目开发的方法得到解决。该项目创造的知识转移将通过与行业的持续合作来实现；在ASME会议上组织可靠性和设计专题讨论会；同行评议的期刊出版物；在主要会议和机构发表演讲和出版物；还有学生教育。教育目标包括招收一名来自少数族裔的女博士生；在升级设计和可靠性课程中实施本项目的软件工具；并编写了一本全面的教科书。

The objective of this research project is to develop new computational methods for uncertainty propagation, reliability analysis, and design optimization of complex engineering systems. The proposed effort will be based on: (1) new dimension-reduction methods for calculating second-moment characteristics of random response; (2) new dimension-reduction and moment-based stochastic methods for reliability analysis; and (3) new algorithms for reliability-based/robust design optimization of structural and mechanical systems. The proposed methods are novel and will be able to address highly nonlinear input-output transformations; unlimited number of random variables or processes; and arbitrarily large uncertainty of input, yet will predict both response moments and reliability accurately. Potential engineering applications include ground vehicle design for durability; fatigue and fracture design of aerospace structures; and design of microelectronics packaging systems. From a fundamental point of view, the dimension-reduction methods will provide an accurate and efficient solution to a general multi-dimensional integral over an arbitrary region. Hence, many problems in basic and applied sciences, which involve uncertainty and/or require evaluation of such integrals, will be solved by the methods developed in this project. The transfer of knowledge created by this project will take place through continued collaboration with industries; organization of symposia on reliability and design in ASME conferences; peer-reviewed journal publications; presentations and publications at major conferences and institutions; and student education. The educational goals comprise recruitment of a female Ph. D. student from underrepresented minority; implementation of software tools from this project in upgrading design and reliability courses; and authoring a comprehensive textbook.